The constitution of visual perceptual units in the functional architecture of V1

Scope of this paper is to consider a mean field neural model which takes into account the functional neurogeometry of the visual cortex modelled as a group of rotations and translations. The model generalizes well known results of Bressloff and Cowan which, in absence of input, accounts for hallucination patterns. The main result of our study consists in showing that in presence of a visual input, the eigenmodes of the linearized operator which become stable represent perceptual units present in the image. The result is strictly related to dimensionality reduction and clustering problems.